Publications related to Hybrid-Spline Dictionaries for Continuous-Domain Inverse Problems

Acoustic DoA Estimation by One Unsophisticated Sensor

Martin Vetterli, Ivan Dokmanic, Dalia Salem Hassan Fahmy El Badawy

We show how introducing known scattering can be used in direction of arrival estimation by a single sensor. We first present an analysis of the geometry of the underlying measurement space and show how it enables localizing white sources. Then, we extend t ...

Springer Verlag2017

Sparsity-Based Data Reconstruction Models for Biomedical Imaging

Emrah Bostan

We propose new regularization models to solve inverse problems encountered in biomedical imaging applications. In formulating mathematical schemes, we base our approach on the sparse signal processing principles that have emerged as a central paradigm in t ...

EPFL2016

Representer Theorems for Sparsity-Promoting $ ℓ _{ 1 } $ Regularization

Michaël Unser, Julien René Pierre Fageot, Harshit Gupta

We present a theoretical analysis and comparison of the effect of

ℓ _{ 1 }

versus

ℓ _{ 2 }

regularization for the resolution of ill-posed linear inverse and/or compressed sensing problems. Our formulation covers the most general setting where the s ...

IEEE2016

PURIFY: a new approach to radio-interferometric imaging

Yves Wiaux, Rafael Eduardo Carrillo Rangel, Jason Douglas McEwen

In a recent article series, the authors have promoted convex optimization algorithms for radio-interferometric imaging in the framework of compressed sensing, which leverages sparsity regularization priors for the associated inverse problem and defines a m ...

Wiley-Blackwell2014

Poisson Image Reconstruction With Hessian Schatten-Norm Regularization

Michaël Unser, Stamatios Lefkimmiatis

Poisson inverse problems arise in many modern imaging applications, including biomedical and astronomical ones. The main challenge is to obtain an estimate of the underlying image from a set of measurements degraded by a linear operator and further corrupt ...

Ieee-Inst Electrical Electronics Engineers Inc2013

Hessian-Based Regularization For 3-D Microscopy Image Restoration

Michaël Unser, Aurélien Bourquard, Stamatios Lefkimmiatis

We investigate a non quadratic regularizer that is based on the Hessian operator for dealing with the restoration of 3-D images in a variational framework. We show that the regularizer under study is a valid extension of the total-variation (TV) functional ...

Ieee2012

Hessian-Based Regularization for 3-D Microscopy Image Restoration

Michaël Unser, Aurélien Bourquard, Stamatios Lefkimmiatis

We investigate a non quadratic regularizer that is based on the Hessian operator for dealing with the restoration of 3-D images in a variational framework. We show that the regularizer under study is a valid extension of the total-variation (TV) functiona ...

IEEE2012

Differential Phase-Contrast X-Ray Computed Tomography: From Model Discretization To Image Reconstruction

Michaël Unser, Masih Nilchian

Our contribution in this paper is two fold. First, we propose a novel discretization of the forward model for differential phase-contrast imaging that uses B-spline basis functions. The approach yields a fast and accurate algorithm for implementing the for ...

Ieee2012

Differential Phase-Contrast x-Ray Computed Tomography: From Model Discretization to Image Reconstruction

Michaël Unser, Masih Nilchian

Our contribution in this paper is two fold. First, we propose a novel discretization of the forward model for differential phase-contrast imaging that uses B-spline basis functions. The approach yields a fast and accurate algorithm for implementing the fo ...

IEEE2012

Compressible distributions for high-dimensional statistics

Volkan Cevher, Rémi Gribonval

We develop a principled way of identifying probability distributions whose independent and identically distributed realizations are compressible, i.e., can be well approximated as sparse. We focus on Gaussian compressed sensing, an example of underdetermin ...

Institute of Mathematical Statistics2012

Hybrid-Spline Dictionaries for Continuous-Domain Inverse Problems

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Acoustic DoA Estimation by One Unsophisticated Sensor

Sparsity-Based Data Reconstruction Models for Biomedical Imaging

Representer Theorems for Sparsity-Promoting $ ℓ _{ 1 } $ Regularization

PURIFY: a new approach to radio-interferometric imaging

Poisson Image Reconstruction With Hessian Schatten-Norm Regularization

Hessian-Based Regularization For 3-D Microscopy Image Restoration

Hessian-Based Regularization for 3-D Microscopy Image Restoration

Differential Phase-Contrast X-Ray Computed Tomography: From Model Discretization To Image Reconstruction

Differential Phase-Contrast x-Ray Computed Tomography: From Model Discretization to Image Reconstruction

Compressible distributions for high-dimensional statistics

Acoustic DoA Estimation by One Unsophisticated Sensor

PURIFY: a new approach to radio-interferometric imaging

Poisson Image Reconstruction With Hessian Schatten-Norm Regularization

Sparsity-Based Data Reconstruction Models for Biomedical Imaging

Compressible distributions for high-dimensional statistics

Hessian-Based Regularization for 3-D Microscopy Image Restoration

Differential Phase-Contrast x-Ray Computed Tomography: From Model Discretization to Image Reconstruction

Representer Theorems for Sparsity-Promoting $ ℓ _{ 1 } $ Regularization

Hessian-Based Regularization For 3-D Microscopy Image Restoration

Differential Phase-Contrast X-Ray Computed Tomography: From Model Discretization To Image Reconstruction